Unassigned · 2026-09-30
Inferring Soil Friction Angle from Robot Foot-Ground Force Histories: A Bayesian Inverse Approach to Proprioceptive Soil Sensing
Dawei Xu, Zhijie Wang
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TL;DR
The authors test whether dry, cohesionless soil internal friction angle ϕ can be identified from proprioceptive foot–ground force histories. They generate a 2D plane-strain continuum forward model (MPM) for a rotating leg, benchmark it against measured rotating-leg force histories, fit two Gaussian-process surrogates (one per force component), and perform Bayesian inversion over the full history. In matched-model recovery, 14 off-grid friction angles are recovered with median absolute error ~0.1° (max ~0.7°).
Why it matters
The paper targets whether routinely available onboard leg-force estimates can carry a quantitatively recoverable signature of a physically interpretable soil parameter (friction angle). If identifiable, proprioceptive soil sensing could feed physics-grounded world models for robot training and support applications like post-wildfire slope assessment.
Method
- Construct a 2D plane-strain continuum forward model of a rigid rotating leg in dry, cohesionless soil using the material point method (MPM) with a Drucker–Prager constitutive model; benchmark against measured rotating-leg force histories by digitizing Li et al. [22].
- Represent the forward map from friction angle ϕ to horizontal and vertical force histories using two Gaussian-process (GP) surrogates trained on the simulation library; resample each force history into an observation vector (Fx and Fz over M=40 angles).
- Infer ϕ via Bayesian inversion with MCMC, using the GP surrogate forward map and reporting posterior medians and equal-tailed credible intervals; evaluate matched-model recovery on 14 off-grid friction angles.
Limitation
The study is limited to homogeneous, dry cohesionless soil and one straight-leg geometry; closing the gap to field measurement requires extension to three dimensions, a foot- and gait-specific forward model, and validation against independent direct-shear or penetration ground truth.
Abstract (from arXiv)
Foot-ground interaction signals recorded by quadruped robots may enable spatially distributed, in situ characterization of soil strength. As a first step, we test whether the internal friction angle $\phi$ of cohesionless soil can be identified from the force history of a simplified rotating leg. A two-dimensional continuum model implemented with the material point method, benchmarked against measured rotating-leg force histories, generates the training data, and two Gaussian-process surrogates support Bayesian inversion of the full histories. In matched-model experiments, the framework recovers 14 off-grid friction angles with a median absolute error of approximately $0.1^\circ$ (maximum $\sim 0.7^\circ$); the reported credible intervals contain the true value in every case. These results establish that $\phi$ is identifiable when the forward model is correctly specified, and support further development of proprioceptive soil sensing for spatially variable terrain, with applications from physics-grounded world models for robot training to post-wildfire slope assessment.